The Nature of Time Anthony Osborne

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THE NATURE OF TIME

By

ANTHONY D. OSBORNE

KEELE UNIVERSITY, UK

An essay concerning the nature of time from the Normal Realist

standpoint


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CONTENTS

Part 1: Questions Regarding the Nature of Time

Section 1: Time and Change..................................................... 1

Section 2: The Discrete Nature of Time...................................... 4

Section 3: The Relative Nature of Time ...................................... 5

Section 4: The Arrow of Time .................................................. 7

Section 5: Time Travel ............................................................. 9

Part 2: Time Dilation in Uniform Motion

Section 6: The Passage of Time................................................12

Section 7: Time Dilation and Time Travel ..................................16

Section 8: Mass Increase with Speed........................................18

Section 9: Minkowski Space-Time.............................................20

Section 10: The Normal Realist Cone Model ...............................21

Part 3: Time Dilation in Orbital Motion

Section 11: The Pope-Osborne Angular Momentum Synthesis(POAMS) ...............................................................................24

Section 12: Time Dilation ion Orbital Motion ..............................25

Section 13: Stellar Collapse and Black Holes ............................27

Section 14: Wormholes in Space-Time and Time Travel .............31

Part 4: Space and Time on a Cosmological Scale

Section 15: The Nature of Space on a Cosmological Scale ...........34

Section 16: Time on a Cosmological Scale .................................38

Part 5: Time in Relation to Mankind and Society

Section 17: Time at its Dynamical Cutting Edge.......................42

Notes and References..........................................................44


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THE NATURE OF TIME

By Anthony D. Osborne

Part 1: Questions Regarding the Nature of Time

Section 1: Time and Change

Man has always been aware of the passing of time, by noticing thepassing of days and nights, the changes in the seasons, ageing,birth, death, and so on. Even the earliest civilisations constructedcalendars in order to record the days and times of the year [1].

Questions concerning the fundamental nature of time have occupiedthe minds of philosophers, scientists and theologians alike since thetime of the ancient Greeks. For example, is time absolute orrelative? Is time continuous or fundamentally discrete? A famousquote by St. Augustine, dating from almost 2000 years ago reads:

What then is time? If no-one asks of me, I know; if I wish toexplain to him who asks, I know not.

Modern societies generally use the word time in two differentsenses. Firstly, it is used as some agreed (at least locally)conventional label associated with a particular event, as in thequestion, What is the time? Without such a conventional label,there would be chaos in human society. Secondly, it is used in thesense of the passing of time, i.e.duration, such as a journey taking

two hours. However, the first meaning is essentially a special caseof the second, since the time represents, of course, the passage oftime after an agreed temporal reference. For example, when we sayit is 11.00 am on the 26th July 2008, what we mean is that elevenhours have passed since twelve oclock the previous night, whichoccurred at the end of the 206th day of the year 2008. In turn, 2008is a label in the Christian calendar for the 2008th year since the birthof Christ. (Of course, this is not quite so, due to complicationsarising from the change from the Julian to Gregorian calendar in the18th century.) Hence, from now on, we shall be primarily concerned

with time in the sense of duration.


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The nature of time is intimately connected with the phenomenon ofchange. On a practical level, we are aware of the passing of timeonly through observation of change. The nature of time itselfremains elusive, since it is not directlyobservable. We know thattime is passing by observing successive days and nights, the ageing

of our friends and relatives, the change of position of the hands onan analogue clock, the change of display on a digital watch and soon. For Ernst Mach, the passage of time can be recorded onlybyobserving changes. He wrote [2]

It is utterly beyond our power to measure the changes of things bytime. Quite the contrary, time is an abstraction, at which we arriveby means of the changes of things.

According to our Neo-Machian Normal Realist philosophy, scientific

knowledge of the world rests, not on any absolutist, Gods-eye-viewintuitions or precepts about underlying realities (the so-calledrealism of classical physics) but always on our very bestinterpretations of phenomena. These phenomena are the onlyphysical reality which is manifest in all the observational (i.e.sensory and instrumental) categories [3]. Hence, in Normal Realism,we follow Machs viewpoint, that time is manifest only in theobservation and recording of change.

The nature of space is as elusive as the nature of time. For

example, stars are separated by the vast expanse ofemptyspace,which means that there is nothing between them. But if space isnothing, then how can it be something we can think and talk about?Once again, according to Normal Realism, we are aware of thespace that surrounds us only by observation and measurement.This awareness comes through observing objects change theirpositions and we extrapolate a mathematical model for spacethrough the measurement of distance between various objects. Inother words, once we have a means of measuring distance, we canset up a three-dimensional Cartesian coordinate system, say, which

describes the position of any point relative to a fixed origin theobserver.

This relationist view naturally extends to our ideas of theuniverse. At its extreme, this view goes so far as to deny the veryexistence of space and time as entities in their own right. Accordingto this view, the universe of space and time is no more than aprojection of human perception that is to say, a construct of pureconvention, with no meaning apart from that.

Certainly from a scientificpoint of view, the only way of studyingthe passage of time is through local measurement. In this sense, it


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makes perfect sense to talk of duration in terms only of dataproduced by some chosen measuring device. This definition ofduration is known as an operational definition [4]. Any questionconcerning time which, in principle, is not answerable byobservation and experiment is dismissed as being not a proper

question for scientific investigation.

Of course, an observer may record the passage of time using anydevice whatsoever, whether that device is one found in nature orin some man-made mechanical or electronic clock. However, inorder to define a unit of one second for example, there has to be anagreed reference instrument, from which all man-made devices maybe set. Then any two observers situated at the same point, usingtwo different recording devices, will agree on the passage of onesecond. At the present time, the frequency of a certain spectral line

emitted by caesium atoms is used to provide a reference frequencyand hence a standard second [5].

We can now, therefore, record passages of time very accurately, infact, far more accurately than distance as measured by a graduatedmeasuring rod. For this reason, radar is often used to measuredistances to a very high degree of accuracy by using the conversionfactor c, traditionally labelled as the speed of light, which convertsobservational time into distance. Using this conversion factor, onemetre is equivalent to 0.000000003335640952 of a second, as

recorded by a caesium atomic clock. This length corresponds to thehistorical definition of one metre as determined by the lengthbetween two marks on a particular bar of platinum kept in Paris [6].

It was the ancient Greeks who were the first to study the nature oftime from a philosophical point of view. We have said, earlier, thatthe passage of time is characterised by change. It was the view ofHeraclitus that change is real, while constancy is a static instant ofthis dynamic change and so only apparent. This is the so-calleddynamic view. In contrast, Parmenides and Zeno argued that

change is only apparent and that constancy is real[7]

. This isessentially the static view, which maintains that all moments intime are equally real and that there is no changing present. In thissense, all times already exist. Zeno presented a number ofparadoxes involving time and motion, the most famous of whichconcerns a moving arrow [8]. He argued, essentially, that since amoving arrow is stationary in any instant of time (the now) it isalways stationary. Following Heraclitus, Aristotle defined time asmotion which can be enumerated. Hence, in answer to Zenosparadox concerning the arrow, Aristotle argued that the flow of time

is the motion of the arrow. The dynamic view of time supported byHeraclitus and Aristotle can be considered historically to be the pre-


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cursor of Machs view and ultimately the Normal Realist view oftime, as presented above. According to this view, the passage oftime is real, so that future times as such do not exist relative to thepresent and events unfold in time.

Section 2: The Discrete Nature of Time

One of the fundamental questions concerning time is whether atime interval is continuous or ultimately discontinuous (discrete).The basic premise in constructing any mathematical model inphysics is that time is continuous. This premise is necessary inorder to be able to use calculus, which is concerned with continuousrates of change. This approach has worked well in most areas ofapplied mathematics, at least on the macro-scale. However, on themicro-scale, quantum theory postulates that time is quantised, i.e.

ultimately discrete, like every other physical measure. This is also abasic premise of our Normal Realist philosophy [9].

As explained earlier, according to Normal Realism, our knowledge ofthe physical world is derived from observation and measurement.Since any measurement is ultimately discrete, we maintain that byusing this operational definition of time, the implication is that timeis ultimately discrete. When we look at the hands on a clock, theyappear to move continuously but when we look closely, they movein a sequence of discrete jumps. All digital time pieces clearly

measure only discrete intervals of time. The most accurate atomicclocks known employ the frequency of vibration of atoms which isultimately a discrete measure.

The fact that we need to suppose that time is continuous in order toconstruct any mathematical model of motion can be squared withthe fact that it is ultimately discrete by using the correspondenceprinciple of quantum theory. This states that, essentially, althoughall physical measures are ultimately discrete on a small enoughscale, these discrete units are so small that the measures appear,

for all practical purposes, to be continuous on the macro-scale.

Although Aristotle maintained the dynamic view of time, he was afour-element theorist for whom all physical measurements werecontinuous. Hence, although the view of time in Normal Realismhas its roots in Aristotles view of the passage of time recorded bychange, its roots also lie in the ideas of Democritus and theatomists involving the discrete nature of physical measures.


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Section 3: The Relative Nature of Time

It is clear that a point in time meaning a label with respect to anagreed temporal reference point must be relative to the observer.For example, it is meaningless to say It is now 11.30 am. Such a

label has meaning only if it is associated with a point in space, toprovide an event. For example, we may say it is 11.30 am inTrafalgar Square in London but at that same moment, it will be 2.30am at Santa Monica Pier in Los Angeles. Before the division of Earthinto time zones in 1884 as a result of an international agreement, agiven time was only relative to a particular town, Glasgow timebeing different from London time for example. This made theinterpretation of railway timetables, for example, veryproblematical! In fact, the advent of the railways was directlyresponsible for this International agreement. Conventional time

labels for events are relative in other ways. For example, when wesay it is the year 2008, this is only relative to our WesternCulture/Christian viewpoint. This year has a different label in theJewish or Muslim calendars.

When we observe the stars from Earth we customarily assume thatwe are observing how they once were, that the information takestime to reach us, the greater the observational distance the greater,in retrospect, is the time. So in this sense, on an astronomicalscale, the present time is only local.

Although it seems obvious that a particular time must be specifiedrelative to an observer, it is not at all clear as to whether thepassage of time is independent or dependent on the observer. Thestudy of this question is apparent in the works of Aristotle. For him,the study of time must involve its measurement, which involves thecomparison with an agreed absolute standard. But how do we knowsuch an absolute standard exists at all points in space, so that it isthe same for all possible observers? Well, we dont. It was Newtonwho first formally proposed that time flows uniformly that it does

not change pace, either at different points in time or relative todifferent observers at different places. In an often quoted passage,Newton states,

absolute, true, mathematical time, (which) of itself, and from itsown nature, flows equably without relation to anything external.

This certainly seems a reasonable supposition to make, the secondpart of it being supported by our everyday experience of time onEarth. However, there is certainly no direct evidence to support thefact that an interval of time is the same for all observers,everywhere at once. Newton began with this particular concept of


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time in order to formulate his laws of motion. His postulate statesthat time is not determined by motion or anything else in nature.Rather, it supposes the existence of an absolute standard clockwhich records time independently of anything else [10]. In the sameway, Newton postulated the existence of an absolute space, which

exists independently of the presence of any observer. This isessentially the realist view of time and space.

Leibniz was quick to realise that Newtons concept of absolute timewas irrelevant to observational science. As appreciated by Aristotle,duration is recorded only by observation. So we need to begin withthe premise that duration is relative to the observer, since we haveno empirical evidence to the contrary. This observational approachagrees fully with our Normal Realist philosophy. Indeed, from apractical point of view, it is not sensible to try to determine whether

two separate events occurring at different places can take placesimultaneously since a finite observer can be at only one place atone time.

Although Poincar was the first to consider relative timemeasurement, it was Einstein who first showed that Newtonsassumption that time flows uniformly, independent of the observer,is at odds with experimental evidence. In particular, he showed thattwo events which are recorded as simultaneous relative to oneobserver will not be recorded as simultaneous when recorded by

another observer moving at a constant velocity relative to the first.Concerning his formulation of Special Relativity, Einstein wrote [11]

My solution was really for the very concept of time, that is, thattime is not absolutely defined but there is an inseparable connectionbetween time and the velocity of light.

According to Einsteins Special Theory of Relativity, duration is arelative measure, and the same is true in our neo-phenomenalistreplacement of Special Relativity. Although, in our Normal Realist

approach, it makes no sense to talk of the velocity of light, there isan inseparable connection between observational space and time,given in terms of the conversion factor c. The consequences of this,in terms of the time dilation effect, are discussed in the following,Section 6.

The question as to whether or not the passage of time can changerate from one time period to the next is probably not a question forempirical science. In 1898 Poincar wrote a paper in which heposed the question of whether or not a time interval of one second

today is the same passage of time as one second a thousand yearsago. It certainly does not appear likely that an observer would be


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able to compare an interval of, say, one second over long periods oftime. So it is not surprising that Poincars question still remainsunanswered.

Section 4: The Arrow of Time

Time differs fundamentally from space in two different ways. Firstly,it is one-dimensional rather than three-dimensional, and secondly,it is anisotropicwhich means that the passage of time flows in onedirection only, from the past to the future. In other words, there isa privileged temporal direction; the passage of time cannot bereversed. This privileged direction is generally known as the arrowof time. We all have everyday experience of this asymmetricalnature of time. For example, we know that if we throw a ball at awindow, we may smash it, but we never observe a window mending

itself and ejecting a ball back into our hands. Of course, we mayrecord a video of someone throwing a ball and smashing a window.Running this video backwards shows the ball being ejected from thewindow and the window mending itself. But this copy of reality isnot reality itself and the reversal of the video players process doesnot reflect a reversal of time. It is, of course, simply that the videostills are presented in reverse order. Note that, in any case, it ispossible to run the film backwards only because in real time the ballhas already been thrown through the window. As another example,as human beings we are starkly aware of the arrow of time

through the realisation that the ageing process cannot be reversed.

Duration appears to be the only physical measure which isunidirectional. As a one-dimensional measure, it can only increase,whereas other measures, such as mass, distance, and energy, candecrease as well as increase. Hence, the distinction between thepast and future (relative to an observer) is much more fundamentalthan between left and right, up and down, heavier and lighter etc.

The obvious question, then, is why should the flow of time be

unidirectional in this way? From our Normal Realist standpoint, thepassage of time is recorded through observation of change and anyobservation depends on information. In this way, as time passes,we gather ever more information. The fact that this accumulatedamount of information can never decrease provides an indication ofwhy time is anisotropic. There are also other considerations whichhighlight the asymmetry in the passage of time [12]. One primaryconsideration is that of causality. The anisotropic nature of time isillustrated by the rule that a cause always precedes an effect. Forexample, the act of pressing a light switch will cause the light to

come on but not conversely. What we do can direct the future butnot the past, which remains fixed. Another consideration is that we


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may obtain a detailed and reliable knowledge of the past but not ofthe future.

A principal reason for the arrow of time is generally argued to bethe Second Law of Thermodynamics. This law appears in various

forms which can be shown to be all equivalent. Basically, it statesthat in any isolated system, entropy, a measure of disorder,increases with time [13]. In other words, this law states that withany change, the order of a system decreases, i.e. that significantorder becomes less probable. Hence, as time flows on it is moreprobable that a system will be in a disordered state than an orderedone. Think of constructing a Lego model from a large number ofsmall pieces. The ordered state of the completed model is uniqueamong all the possible combinations of the pieces and is highlyunlikely to occur at random. Otherwise, without the modeller, there

are a huge number of disordered states uncompleted or wronglycompleted models. This increase in disorder over time is manifest innature as the process of decay.

The Second Law of Thermodynamics was originally proposed byClausius in the middle of the 19th century. This was really the firstphysical law which reflected the asymmetrical nature of time. Untilits appearance, all physical laws, such as Newtons Laws of motionfor example, were symmetrical in time [14].

It should be noted, however, that there are localised exceptions tothis Second Law. For example, crystals can grow in certain chemicalsolutions, representing an increase in order, but such instances arerelatively rare. In this sense, the Second Law applies globally ratherthan locally. In other words, it is generally postulated that, overall,the net disorder increases with time, although there may be localexceptions. Nevertheless, there are problems associated with usingthe apparent general increase of entropy as the sole basis for timesanisotropic nature [12]. Some theoretical physicists and philosophersargue that the Second Law cannot be projected to the universe as a

whole. Others argue that just because the Second Law appears tobe true at the moment, it need not be valid for all time. Some go asfar as to believe that time may eventually be reversed, when, forexample, the universe begins to collapse, which they call the heatdeath of the universe! However, to say the law of entropy isuniversal is not logically the same as saying that the universe, assuch, is subject to the law of entropy.

A full philosophical discussion of the asymmetry of time is providedin reference 12.


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Section 5: Time Travel

The aspect of time which fascinates people the most is thepossibility of time travel. In this respect, the nature of time isfundamentally different from the nature of space. In space, it isclear that we may travel in any direction we wish and vary ourspeed. Initial thoughts concerning time generally tend to suggestthat it is not possible to travel back in time or to vary the rate atwhich we persist through time. However, let us examine thepossibility of time travel a little more carefully. First, we need to beclear as to what we mean by time travel. In one sense, we are alltravelling in time into the future simply by persisting. We havediscussed, earlier, some of the reasons why time has to be arelative concept, so it makes sense to talk of time travel only inrelation to some reference clock (any suitable timepiece).

Consider, then, a fixed standard clock at a particular point in space.The time as recorded by this reference clock is usually called thecoordinate or externaltime that is, objective time, as opposed tosubjective time, or time as we sense it. Now consider an observerA, standing relatively stationary at this fixed point in time and spaceand whose clock is synchronised with this standard clock. Weassume thatAs clock always records the standard passage of timerelative to himself, that it is not reset in any way and does not losetime or stop, etc. This time as recorded by As clock is generallyknown as his, i.e., As,propertime. If, after some passage of time

as recorded by As clock, the reference clock and As clock are nolonger synchronised, then A may be said to have time travelledrelative to that fixed reference clock.

Under this criterion, if it were technologically possible to place aliving person in cryogenic suspension and then revive that person,say a thousand years from now, this would notbe classed as timetravel in the sense we have discussed. It would be simply that thisperson has lived longer than everyone else because his/herbiological clock has temporarily stopped. A clock placed with that

person but not cryogenically suspended will record the samepassage of time as that of the fixed reference clock. The situation issimply that the persons life-processes have been suspendedthroughout all the intervening years without his being conscious ofit.

There are two basic possibilities for time travel. One is the idea of atime-slide, in which the time traveller, due to relative motion,passes through all the intervening times as recorded by the fixedreference clock but at a different rate. This sort of time-slide into

the future is now accepted by the majority of mainstreamphysicists. Any such trip is by no means logically problematical


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since it cannot causally undermine what has already happened. Thetime dilation effect predicted in Special Relativity and our NormalRealist alternative of that theory, which is firmly supported byempirical evidence, shows that time-slides into the future are bothlogically and physically possible [15]. This is demonstrated in the

following, Section 6. Both General Relativity and POAMS (the Pope-Osborne Angular Momentum Synthesis), our neo-phenomenalistalternative to that theory, show that time-slides into the future canalso be caused by the presence of a massive body [16].

This first idea, then, is that of the time-slide. The other idea whichdeserves a mention is that of the time-jump, in which the travellerdoes not pass through the intervening years [17]. This will bediscussed in due course. Meanwhile, let us consider, in contrast totime-slides into the future, the possibility of time travel into the

past. To say the least, this appears to be highly improbable due tothe fact that it creates the possibility of changing events that havealready taken place, which involves backward causation. Usually wethink of an effect as preceded by a cause. Initial thoughts,therefore, tend to suggest that time travel into the past is logicallyunsound.

However, we must be careful not to jump too quickly to conclusionshere. For example, it has been argued that a type of backwardscausation occurs in quantum theory. According to that theory, the

state of a quantum system is indeterminate in certain respects, untila measurement is conducted, the action of which determines acollapse of the wave function into physical actuality [17].Nevertheless, what has been said about the asymmetry of timeindicates that an actual time-slide into the past is not possible,which rules out backwards causation.

However, let us now investigate a little more carefully the otherpossibility, namely that of a time-jump into the past. According tothe static-block, or Parmenidean view of time, events which occur

at a given (coordinate) time are fixed and cannot be changed[17]

.So the argument which says that, at least logically, time travel intothe past is possible goes something like this. A time traveller cannotchange the past since his or her existence at a particular point intime has alreadyhappened (in objective or coordinate time, that is).The time traveller obviously cannot recall being there previouslysince that event is still in his or her future. For example, a mancannot travel back to, say, a week earlier in time and at that sametime meet himself at that point whilst already aware, from hisfuture knowledge of what has already happened that he did notmeet himself at that point. A woman cannot go back and kill herown mother before she was born, since that woman was born ...


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and so it goes. In other words, we do not have the freedom tochange history in which whatever we choose to do is already doneand dusted. This is related to what is sometimes known as thechronology protection conjecture, according to which the laws ofphysics conspire, as it were, to prevent (macroscopic) events in

the present moment from carrying information into the past.Although logicallyor purely theoretically possible, any such idea ofactualtime travel into the past still seems, to say the least, highlyunlikely since it confounds the known laws of physical causality.

Despite this caveat of the physical impossibility of backwardcausality, some writers have shown that time travel into the past islogically possible by creating multi-dimensional models of timewhich project all possible pre-determined futures branching-off fromany actual event. However, we have no solid reason to suppose that

time is like this. Nevertheless, theories involving the possibility ofparallel universes are popular, especially with writers of sciencefiction. If time travel into the past were to take the form of passingfrom one universe to another, then there would be no logicalcontradiction in that view; each jump into the past would createanother possible future universe. However, this scenario does notinvolve travelling into ones own past and so may be discounted astime travel in the strict sense. Most philosophers are agreed that inany model which supposes a one-dimensional time and a singleuniverse, time travel into the past entails unavoidable logical

paradoxes[17]

. For example, if a person was able to time-jumpfreely and return to a time when he already existed, there wouldthen be two of him at that time, but a person cannot possiblyoccupy the same point in time more than once. After all, if thatwere the case, then he could travel forwards and then back to theearlier time again and again to create three of him, four of him andso on which, logically, is a reduction to absurdity!

Of course, there is a huge difference between a scenario beingtheoretically possible and that scenario being physically possible.

One can propose any number of postulates one wishes, but in orderto have a scientific theory rather than a metaphysical one, theimplications of that theory have to be susceptible of beingempirically verified. According to both Special Relativity and ourneo-phenomenalist alternative, time travel into the past is notphysically possible [16]. In contrast, some theoretical physicistsbelieve that General Relativity allows for the possibility of time-jumps into both the past and the future, whereas our alternativeapproach in the form of POAMS does not [18]. We will return to thisquestion later.


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Part 2: Time Dilation in Uniform Motion

Section 6: The Passage of Time

As we have stated in Section 3, the passage of time may varybetween different observers, so that duration is relative, notabsolute. Prior to the advent of Special Relativity in 1905, it wasgenerally assumed that the passage of time was an absolutequantity, since everyday experience did not indicate otherwise. Butas we have seen, once we know that there is a universal constantconversion factor, c, which determines a constant relationshipbetween observational time and distance for all observers, itbecomes plain that the passage of time must be relative to theobserver. Two observers moving at some significant speed v

relatively to each other in space can never agree on the timeinterval between two events occurring at particular observationaldistances and times. This is essentially because the opticalinformation regarding each event directly reveals a relative time-lagin the object in accordance with its distance, in the constantdistance-time rate c, which is the same for all observers. That is tosay, in the telescope of an observer, an identical clock which is, say,300,000 kilometres away will be seen to read one second of timeearlier than his own clock, while another identical clock twice thedistance away will be seen to read two seconds behind, and so on.

Hence, for observers in uniform relative motion, events that occursimultaneously relative to one cannot occur simultaneously toanother [19]. This should become perfectly plain in due course.

We can obtain an explicit formula for the passage of time asrecorded by a relatively moving clock in terms of the same passageof time recorded by a fixed reference clock. This is by using theconversion factor cplus some simple geometry and algebra [16]. Forinstance, consider a body X which moves uniformly (i.e. withconstant speed, vsay, in a fixed direction) relative to an observer

situated at some fixed point O. In classical physics, the distance, s,ofX relative to O at any time t, is described by a straight lineplotted against two perpendicular axes, labelled s and t. This linehas a constant gradient v= s/tand ifXpasses O at time t= 0,then this line passes through the origin. The equation of this line isthen s = vt, as shown in Fig. 1(a), below. In other words, after timethas elapsed forX, he is at a distance vtfrom O. This passage oftime is the same as viewed by all observers ofX regardless ofdistance or relative motion. Note that in classical physics, Xand Orecord the same passage of time.


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In Fig. 1(a), there is no special significance attached to the length

of the line with equation s = vtfor a given value oft, since in thistraditional kind of representation there is no fundamentalinterconnection between distance and time as such. Taking intoaccount our postulate that there is an observer-independentconversion factor, c, which converts observational distance intoobservational time and vice versa, this situation is radicallychanged. In this case, a fixed geometrical relationship is establishedbetween the dimensions ofs and t. Hence, it is to be expected thatwith this overall connection, motion must affect time in some way.This is because motion is now a geometricalcombination of time

measures, analogous to the lengths which determine an ordinaryarea. In contrast to classical physics, however, we do not assumethat time is observer-independent. In this case, the naturalmeasure of the passage of time, t, is as recorded by a clock whichmoves with the body X, since this is the only time measureassociated withXwhich is independent of the time of the observer.

To reiterate, the body X travels a distance s measured in metresrelative to O in a time t recorded in seconds by Xs clock. Thisdistance s can also be measured in seconds by the use of the

conversion factor c. Then the distance-time diagram, Fig. 1(a),becomes the two-dimensional time diagram, Fig. 1(b). In this latterfigure, the two axes (labelled s/cand t) are both measured in unitsof seconds. Bearing in mind that the line segment OX representsthe path ofXs clock relative to O, it follows, therefore, that thelength of OX in this second diagram is the resultant time tR, asrecorded by O, forXs clockto reach its position relative to O afterits time t. Then tR will be simply the length of the hypotenuse of thetriangle in Fig. 1(b), given by Pythagorass theorem as

tR

2 = t2 + (s/c)2

s = vt

tR

(a) (b)Ot tO

body X

s/c

body X

Fig.1: Time Dilation in uniform motion

s s/c

t t


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Now the speed, v, ofX relative to O (i.e., relative toOsclock) isgiven by v= s/tR, so that,

tR2 = t2 + (vtR/c)

2

Re-arranging then gives

t2 = tR2 (v2/c2 )tR

2

and hence,

t= (1 v2/c2) tR (TD)

Equation (TD) is known as the time dilation formula and is thesame, here, as the standard formula derived in Special Relativity by

different means [20].

The formula (TD) gives the time t as registered on a relativelymoving clock in terms of the time, tR, registered on an observersclock. For any non-zero relative speed v, which is less than c, thefactor (1 v2/c2) is less than 1, so that this formula shows that amoving clock runs slower and so is time-dilated relative to anobservers clock. Hence, the formula clearly shows that the passageof time is relative to the observer. Equation (TD) also indicates thatc cannot be treated as if it were a speed since, otherwise, for v

equal to c, t is zero, independently of the observer time tR. In thiscase, the travelling clock would register no time at all, regardlessof how great the distance travelled might be. This resultant timetR, as registered by the observer, O, is, for obvious reasons, knownas the observational time or sometimes as coordinate time. Thecorresponding time, t, registered by the moving body itself, asviewed in his telescope and/or spectroscope is, the proper time ofthat body.

It should be emphasised, here, that this time dilation is a relative

effect, not an absolute one. If we imagine X to be the observer,then O moves uniformly relative to X with speed v, so thataccording toX, it is Os clock which appears to run the slower of thetwo. There is no contradiction here since this is a relative effect.Indeed, there is only an apparent contradiction if we try to think ofthe effect in terms of both O andXtogether, in a Gods-eye-viewway, at the same time. In our Normal Realist philosophy, this is notpossible since there is no such Gods-eye-view which we canlegitimately presume to take, all phenomena being ultimatelydependent on the finite, point-centred observer.


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According to the scientific operationaldefinition of time, the onlyway that we may study the time dilation effect is through therecordings of clocks. But does a moving clock running relativelymore slowly imply that time itself is running relatively more slowly?In theory, one way to address this question is to study the effect of

time dilation on biological ageing due to relative motion.Unfortunately, due to the present state of our technology, we arenot yet in a position to do this. However, a clock represents anydevice capable of recording a passage of time. This includesbiological clocks, so that there is no reason to suppose thatbiological ageing should be exempt from time dilation. In otherwords, a space-traveller moving uniformly relatively to Earth shouldage at a slower biological pace than the rest of us that is to say,relative to us.

When Einstein first discovered the time dilation formula, hestruggled with some of its philosophical implications. In particular,since it implies that the recording of time is always relative to aparticular observer, how can we attach any meaning to now? Heeventually concluded that now, meaning something essentiallydifferent from past and future, was a human concept rather than ascientific one [2]. Einstein wrote:

there is something essential about the now which is outside therealm of science.

The time dilation result clearly does not agree with what we usuallythink of as commonsense, but this is only because, since anyspeed necessary to detect an effect lies beyond our everydayexperience. However, this time dilation has been verified byexperiment, beyond reasonable doubt. One of the first suchexperiments was performed by Ives in 1938. He measured thefrequency of vibration of hydrogen atoms when at rest relative tothe laboratory and again when they were moving at a speed of1760 kilometres per second. Ives found that the frequency

decreased, corresponding to an increase in time per vibration. Thisincrease in time per vibration was exactly the amount predicted bythe formula (TD)[21].

Another of the earliest verifications of the time dilation effectconcerns elementary particles known as muons. These occur inappreciable numbers in the Earths upper atmosphere and areunstable; they decay with a mean lifetime of approximately 2.2 10-6 seconds when observed at rest. Muons have a speed of about0.9965c relative to an observer on Earth, so that according to

classical physics, the mean distance that the high altitude muonscould cover before decaying is about 650 metres. In that case, the


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high altitude muons should not be detected at sea level. However,muons are, in fact, found in significant numbers at sea level, as firstdetected in experiments performed by Rossi and Hall in 1941[22].The explanation is that with v = 0.9965c and t = 2.2 10-6

seconds, (TD) gives the muons a mean lifetime of tR 2.64 10-5

seconds, relative to Earth. Hence, the high altitude muons are ableto travel a mean distance of about 7.9 kilometres before decaying,relative to Earth and so can easily reach Earths surface, asobserved.

Section 7: Time Dilation and Time Travel

The time dilation formula, (TD), implies that (human) time travelinto the future as a time-slide (see above) is an actual theoreticalconsequence of relativity theory. For the moment, we shall consider

a theoretical scenario and discuss the practical difficulties later.Suppose that a space traveller Tsets off from Earth in a spacecraftand after an initial period of acceleration, in order escape theEarths atmosphere and to increase his speed to 0.6c, he travelsuniformly at constant speed 0.6crelative to Earth. Suppose Tvisitsa planet, a distance of, say, three light-years away before reversinghis motion and returning to Earth with an opposite uniform velocityat the same constant speed 0.6c. Note that Thas to decelerate andaccelerate again in order to visit the planet whereas the terrestrialobserver of the motion does not. Let us assume that the time T

spends on the planet is very short compared to the rest of his trip.Then according to an observer, E, on Earth, the space traveller Ttakes tR = 6 0.6 = 10 years to complete the round trip. However,ignoring the very short periods of non-uniform motion on take-offand touch-down, according to (TD) with this value of tR andv = 0.6c, the time recorded by T for the round trip on clocksrelatively stationary to himself (including his own biological clock) isonly t= 0.8 tR = 8 years. Hence, when Treturns to Earth, he haseffectively returned two years into the future relative to Earth time.He has time-slid into the future since two extra years have passed

on Earth where everyone has aged an additional two years relativeto the traveller. The time dilation formula, (TD), shows that thefaster Tis able to travel, the greater the time-dilational effect, andthe further he is able to travel, the longer is the period of the timeslide into the future. For example, ifTcould embark on a round tripof 1000 light years at a speed of 0.998c, then he would return toEarth after 1002 terrestrial years, whereas the trip according to hisown clock would only take about 63 years! When he returned toEarth all of his family and friends would have died long ago, so sucha trip may not be very appealing to contemplate!


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A famous controversy which has surrounded the time dilationformula, (TD), from soon after its first appearance, is the so-calledclock paradox or twins paradox[23]. Consider the same scenarioas outlined above, where, now, the space traveller, T, and the Earthobserver, E, are identical twins, who are exactly the same age

before Tbegins his round trip in space. After the trip, Tmeets upagain with his stay-at-home brother E. Ignoring the accelerationsand decelerations on take-off and touch-down, it follows by (TD), asabove, that when the twins meet up again, T will be relativelyyounger than his twin E.

The alleged paradox is this. Initial thoughts suggest that Tcouldclaim with equal right that it was he who remained where he was,while it was Ewho went on the round trip, with the consequencethat E should be the younger when they meet again. However,

there is no such paradox, because it must be remembered thatequation (TD) applies only to relatively uniform motion. As long as Tcontinues to move uniformly away from E, then each observersclock runs slower relative to the clock of the other. However, inorder to compare clocks, Thas to go on a round trip and return toEarth. In order to make this trip, Thas to undergo an initial periodof acceleration and when he reverses direction to return to Earth(even if he does not visit a planet) this necessarily involves a periodof deceleration and acceleration, which has definitely observableand measurable physical, (e.g. visceral) effects. In contrast, the

observer Ewho remains on Earth does not experience these effectsof non-uniform motion. Hence, the observational frames ofEand Tare not physically (and so not mathematically) interchangeable. Insummary, there is no paradox, since the argument that there is aparadox assumes a symmetry between the frames which, in fact,there cannot be.

It follows, then, that although (TD) applies for most of the journeyofTrelative to E, the periods of acceleration and deceleration ofT,no matter how short compared to the length of the whole journey,

destroy the otherwise symmetrical situation between E and T. Agood analogy for the fact that very short periods of non-uniformmotion have a huge impact on the whole journey has been providedby Bondi. Imagine, he says, travelling in a car at a constant speedalong a straight road. Suppose at some point, the car turns rightand continues to travel at constant speed along another straightroad. Even though the period of non-uniform motion, when the carturns right, is negligible, it has a very large effect on the carsdestination!

There is another way to think of why Ts initial acceleration makes arelatively large contribution to the eventual age difference between


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Tand E. At the end ofTs initial acceleration to speed 0.6c, say, heis transferred to an inertial frame relative to which the distance hehas to travel has alreadybeen shortened by a factor of 0.8. So afterthis brief period, he has to travel a distance of only 8 light-years,relative to himself, rather than 10 light-years.

In conclusion, it can be shown that it is the space-traveller T thatages less than his stay-at-home brother Eafter Ts round-trip [24].The fact that there is no paradox and that it is Twho ages less thanE is firmly supported by empirical evidence. For example, as wehave seen, those experiments that involve accelerating muonssupport this conclusion [25]. Another set of experiments whichverified both the time dilation formula (TD) and the conclusion ofthe twins paradox were performed by Hafele and Keating in 1972.Such experiments involved monitoring atomic clocks carried on

commercial jet flights around the Earth, both in easterly andwesterly directions. It was found that the moving clocks registereda time period less than relatively stationary clocks when the jetsreturned, by an amount predicted by (TD) [26] [27].

Note that although formula (TD) indicates that time-slides into thefuture are theoretically possible, since relatively moving clocks areslowed it provides no information with regard to time-slides into thepast. As stated previously, according to our Normal Realistapproach which takes into consideration the unidirectional nature of

time, time-slides into the past are not possible. This conclusion iscertainly not contradicted by (TD). Of course, when we look out intospace, we are looking into the past of objects by observing eventsthat, in the classical way of thinking, have already happened, since,in that way of thinking, the information regarding those eventstakes time to reach us. This time delay is determined by theobservational distance/time conversion factor c. So in order totravel back in time by travelling in space, we would have to exceedthe universal speed limit of c, which according to both SpecialRelativity and our Normal Realist alternative to that theory, is not

possible.

Section 8: Mass Increase With Speed

We have shown how the time dilation formula, (TD), makes timetravel, in the sense of time-slides into the future a proven fact. Thishas been recorded in experiments involving elementary particlesand tiny time differences registered on relatively moving atomicclocks. However, in order for a human space-traveller to travel intothe future in the way described in the last section, we would have to

be able to accelerate macroscopic objects up to appreciablefractions ofc. To accelerate such an object requires energy. Such


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energy is used when work is done in producing a force. The greaterthe mass of a body, the greater has to be the magnitude of theapplied force in order to produce a given magnitude of acceleration.The force needed to accelerate a human being to the extent ofexhibiting appreciable time dilation would be far greater than

human flesh could ever stand.

Now, both Special Relativity and our Normal Realist alternativepredict that the effective mass of a relatively moving body increaseswith its speed. To be specific, suppose that an observer O observesa bodyXof constant mass moving uniformly with constant speed v.Let the mass ofX, as recorded by an observer travelling with Xbem0 (known as the rest mass ofX) and the mass ofX, as recordedby O, be mR. Then

[28]

mR = (1 v2/c2)-1/2m0 (MI)

Note that for non zero v, mR is greater than m0, so that a body inrelative uniform motion has a larger mass relative to the observerthan that recorded in its own rest frame. (Compare formula (MI)with formula (TD).)

The fact that mass increases with speed was first detected byKaufmann and Bucherer in the early 1900s. While investigatingbeta ray radiation, they found that the speeds with which

elementary particles were ejected from different radioactivesubstances were appreciable fractions ofcand that the greater thespeed, the greater the effective mass of the particle. Using (MI),they found that the restmass of each particle was the same andequal to the standard rest mass of an electron. They alsodiscovered that each particle had the same electric charge as anelectron and so concluded that beta ray radiation was caused byelectrons being ejected at high speeds from radioactive materials[29].

It follows, then, from formula (MI) that the greater the speed of amoving body, the greater the magnitude of the force, and hence thegreater the energy required to accelerate it, and the more energythat is imparted to the body the more massive it becomes. Thismeans that we would need an enormous amount of energy toaccelerate a macroscopic object, such as, for example a bullet or ahuman body, up to any appreciable fraction of c; more energy, infact, than we could possibly supply. The formula (MI) shows that itis certainly not possible to accelerate objects right up to speed c,since this would require an infinite amount of energy, resulting in aninfinite mass. This is another reason why c cannot sensibly beinterpreted as a speed. From a practical point of view, then, it


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would be very difficult for a human being to travel significantly intothe future. Besides, the g force experienced by a space traveller inaccelerating up to an appreciable fraction of cwithin a reasonableperiod of time would, as we have said, not be physically survivable!

Section 9: Minkowski Space-time

We have seen that, according to the time dilation formula, (TD), thepassage of time as well as positions in space are relative to theobserver. It is clearly not adequate, therefore, to talk about aparticular observation of an observer O occurring at a particularpoint in space. Rather, that particular observation must be specifiednot only by its position in space but also by the time at which ithappens relative to O. An observation occurring at a point in spaceand at a particular time relative to O is called an event. Hence,

when we talk of observations, we are really talking about suchevents. In standard orthodox Relativity, the set of all these eventsis known as space-time. The hyphen in space-time conveys thefact that space and time are intimately connected, in the way thathas been described.

Recall that if a clockXmoves uniformly relative to O, with constantspeed v, then (TD) gives the proper time, t, as recorded by X, interms of the observer Os time tR. Remember that the proper time isindependent of any particular observer and so serves as an

absolute, rather than a relative parameter. The set of all events,i.e., space-time, together with proper time t, serving as anindependent parameter, provides a mathematical model forstudying relative uniform motion, known as Minkowski space-time.It is this model which forms the basis of study of relativistickinematics and dynamics [15][28][30]. Minkowski first presented hisspace-time concept in a lecture given in Gottingen in 1907. Hepresented a less technical account at the eighteenth Congress ofGerman Scientists and Physicians in Cologne, in September 1908.He began this now famous second lecture with the words [2]:

The views of space and time which I wish to lay before you havesprung from the soil of experimental physics, and therein lies theirstrength. They are radical. Henceforth space by itself, and time byitself, are doomed to fade away into mere shadows, and only a kindof union of the two will preserve an independent reality.

Now, whether or not Minkowskis space-time exists as a physicalreality, rather than simply as a convenient mathematical model, isan open philosophical question. The substantivalist view is that the

universe is, in reality, truly a four-dimensional space-timemanifold, rather than this space-time simply being a mathematical


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model. (This view is sometimes known as the four-dimensionalitythesis.) In contrast, from our Normal Realist standpoint, we wouldsay that since, from empirical evidence, we cannot determine theanswer to this question of the reality or otherwise of theMinkowskian manifold, and since we have no Gods-eye-view that

we can ever presume to be a party to, we can claim only thatspace-time is no more than a convenient mathematical model ofreality.

Section 10: The Normal Realist Cone Model

Our Normal Realist derivation of the time dilation formula, (TD),provides a three-dimensional model for the phenomenon of timedilation. Recall that (TD) gives the proper time, t, as recorded on arelatively moving clockXin terms of the same passage of time, tR,

as recorded by a relatively stationary observer O. Our derivation of(TD) depends on the relationship between t, tR, and s/c, the latterbeing the observational distance, converted into seconds, travelledbyX, in the time relative to O. This relationship is given by

tR2 = t2 + (s/c)2 (C)

(see Section 6). Ift, s/cand tR are all treated as variables in thisequation, then it represents a right-circular cone in three

dimensions, relative to three mutually perpendicular time axes, t,s/c and tR, respectively. As such, this conic surface represents athree-dimensional graph of time dilation, as shown in the platesbelow. The axis of the cone is the tR axis and its apex is situated at(0, 0, 0). The end and side elevations of such a graph for non-negative values of t, s/c and tR, are shown in Plates 1 and 2respectively. This model illustrates effectively the relationshipbetween any given values oft, s/cand tR and clearly indicates that tis less than tRfor non-zero relative speed v. The larger the value ofs/c, the greater is the difference between tand tR.

For any fixed value oftR, (C) is the equation of a circle of radius tR,centred at the origin. Such circles are shown in the end elevation ofthe cone, as indicated in Plate 1. On the other hand, iftis fixed andthe time-measure s/c is plotted against the time-measure tR, theresult is a hyperbola with equation

tR2 (s/c)2 = t2

Such hyperbol are shown in the side elevation of the cone, as

indicated in Plate 2. As can be seen, any such hyperbola isasymptotic to the lines described by equations s = ctR.


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Plate 1: End elevation: Plate 2: Side elevation:

The Newtonian aspect of motion The Einsteinian aspect of motion

The Conic Surface Graph of Motion

In both Special Relativity and our Normal Realist alternative to thattheory, no information can be transmitted at a speed greater thanc. At first sight this appears to be at odds with the various

Newtonian instantaneous connections such as the universalconservation laws. This is not surprising since Special Relativity andNewtonian physics are not compatible in other ways. However, ourcone model shows there is no conflict between the two theories inthis respect, since both aspects of motion are depicted on the samethree-dimensional (conic) graphical surface. The explanation is asfollows.

There are two distinct speeds associated with the uniform motion ofa bodyXrelative to an observer O. The first is what we can describe

as the Newtonian speed, which is s/t, where s is the distancetravelled by X in its proper time t. The second is what can bedescribed as the Einsteinian speed and is s/tR,where tRis the timetaken forXto travel the distance s relative to Os clock. Our conicrepresentation of time dilation clearly shows how the Newtonianspeed-unlimited graph of physical motion (the end elevation of thecone shown in Plate 1) and the Einsteinian speed-limited aspect(the side elevation of the cone shown in plate 2) can be equallyrepresented with no conflict whatsoever on the same conic surface.What is represented in the end elevation, Plate 1, as a theoretically

unbounded Newtonian speed appears in the side elevation, Plate 2,as the Einsteinian speed limitc. This speed limitcappears as an

tRtR

t

tOO


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asymptote to the graphs representing material particle motion andso, again, is not a speed as such.

Although it was not surprising that Special Relativity appeared to bein conflict with Newtonian physics, much more of a concern during

the 1920s and 1930s was that it also appeared to conflict withquantum theory. According to quantum theory, it is possible, inprinciple, to create a pair of particles with complementaryproperties. Each particle may have either property until theproperty of one particle is recorded by observation. Then quantumtheory states that the other particle must instantly have thecomplementary property, irrespective of the spatial separationbetween the particles [2][30]. Hence, quantum theory implies thatsome type of instantaneousaction-at-a-distance takes place, whichclearly contradicts Special Relativity.

However, in terms of our cone model, there is no contradictionbetween instantaneous action-at-distance and the existence of auniversal speed limit. Our answer to the question as to whetheraction-at-distance is instantaneous or time-delayed is plainly that itis both. In quantum theory, as in Newtonian mechanics, there is, ascan be seen from Plate 1, no limit to the speed at which quantuminfluences may travel between fundamental particles, whereas forrelativists, as can be seen in Plate 2, no physical influencewhatsoever may be conveyed faster than the speed limitc. There

is no contradiction here, since the instantaneity takes place in oneobservational dimension, whereas the time-delay takes place in adifferent observational dimension.

What we are saying here is that an action may have both time-delayed and instantaneous components, without there being anylogical contradiction. A good analogy lies in the running of a film. Inthis case, the instantaneous connection between objects in the stillframes is analogous to the instantaneous component ofinteraction, t,and the analogy of the observationally time-delayed

component tR, is the sequencing of those stills in the running of thefilm. In our Normal Realist approach, this is called the CinematicModel of combined quantum instantaneity and relativistic time-delay.


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Part 3: Time Dilation in Orbital Motion

Section 11: The Pope-Osborne Angular Momentum Synthesis(POAMS)

We have shown in Section 6 that in our Normal Realist approach torelativity, there is a time dilation effect associated with linearmotion, just as there is in Special Relativity. Recall that if tdenotesthe time as registered on a relatively moving clock, X, and tRdenotes the same passage of time as registered on an observersclock, O, then

t= (1 v2/c2) tR (TD)

where vis the constant speed of the clockXrelative to O. We nowinvestigate the effect on time in non-linear motion, in particular inthe orbital motion of the planets, stars and satellites in our solarsystem and beyond.

In Newtonian theory, all free motion, i.e. motion not subjected toany external force, is linear so that observed orbital motion, whichNewton saw as unnatural, is explained by the presence of anunseen in vacuo force of gravity, which distorts the assumednatural straight line paths into orbital trajectories. However, wemaintain that uniform motion is never observed. According to the

Pope-Osborne Angular Momentum Synthesis (POAMS), therefore, incontrast to Newtonian theory, the natural path of any particle is theobserved trajectory followed by the particle when it moves freelyunder the influence of nothing but its own angular momentum. Thisis without any need of supposing the existence of an unseen invacuo gravitational force[31].

Since, in POAMS, the trajectory of any freely moving particle isnaturally orbital, such a particle moves non-uniformly, i.e., it hasnon-zero acceleration, so that its speed is generally not a constant.

We show in reference 31 that the natural trajectory of a particledepends on the mass, M, of the body which it is orbiting. Moregenerally, it depends on the mass of a whole system of bodies,taking the orbital angular momentum of the particle relative to thecentre-of-mass of such a system. These considerations indicatethat, for natural orbital motion, (TD) has to be extended to providea formula for tR which depends on M and, in general, a variablespeed v.

In the hypothetical situation in which all influences are essentially

removed, allowing a particle to move in isolation in empty space,then its trajectory might seem to follow part of a straight line so


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that it would seem to move uniformly, in which case, (TD) wouldapply. In this way, POAMS aligns itself with two of the basicpremises of Einsteins General Relativity [32]: the presence of mattercauses the trajectories of freely moving particles to be non-uniformand orbital, and that to a limited extent, (TD) applies. The second

premise is essentially, Einsteins Principle of Equivalence. BothPOAMS and General Relativity remove the need for assuming an invacuo gravitational force to explain the natural trajectories offreely moving particles. Both POAMS and General Relativitymaintain that the reason we feel a gravitational force on theEarths surface is because our bodies are prevented from followingtheir natural force-free orbit below that surface. Hence, POAMS ismore aligned to General Relativity than it is to Newtonian theory,although it retains some aspects of both theories.

In POAMS, since the paths of freely moving particles are naturallycurved, the geometry of the associated space-time must be non-Euclidean, unlike the Euclidean, absolute space and time envisagedby Newton. In other words, in POAMS, the presence of matterchanges the geometry of space-time, away from Minkowski space-time (see Section 9). This, of course, is also, essentially, the thirdfundamental premise of General Relativity.

However, there are fundamental differences between POAMS andGeneral Relativity. The latter provides a mathematical model in

which the flat space-time geometry of Special Relativity is curveddue to the presence of matter. In contrast, POAMS, with its NormalRealist foundations, begins with the postulate that all free motion isorbital and that, based firmly on observation, angular momentum isconserved. There are also other fundamental differences; notably,that the space-time manifold of General Relativity is continuous,whereas in POAMS, space-time is discrete at the fundamentalquantum level.

Section 12: Time Dilation in Orbital Motion

We now turn to one particular situation: the simplest case of justone particle, P, orbiting a massive body, B, treated as an isolatedpaired and balanced system, that is, with no external effects to betaken into account. This provides a simple model of a planetorbiting the Sun to a good degree of approximation. In this simpleexample, we assume that neither the body B nor the particle P isspinning. In this case, according to Newtonian theory, Ps trajectoryis determined by Newtons laws of motion and his inverse squarelaw relating to his presumed in vacuo gravitational force. These

laws demand that the orbital angular momentum ofPis conserved,and that if the orbit of P is closed, then the trajectory ofP is an


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ellipse [33]. In this way, Newton was able to explain why the planetsmove in elliptical orbits around our Sun, as observed by Kepler.

In complete contrast to Newtonian theory, POAMS begins with thepremise that angular momentum is holistically conserved, so that inthis simple two-body instance, the orbital angular momentum ofPrelative to B is constant. In the case where the orbit ofParound Bis closed, the constancy ofPs orbital angular momentum dictatesthat Pmoves in an elliptical orbit exactly as predicted by Newtoniantheory [34]. To reiterate, in contrast to Newtonian theory, in POAMSthe orbit ofPis the orbit that Pnaturally follows when not subjectedto any external forces or constraints, rather than a non-linear orbitcaused by an invisible in vacuo gravitational force.

We turn now to a replacement for (TD) which applies to the orbital

trajectories of the freely moving particles. Let us first consider thecase of the particle P freely moving in a circularorbit around thebody B, of mass M. We shall consider only the case in which B isstatic (non-rotating etc.) and ideally spherical. In this case, it canbe shown that the proper time, t, recorded by a clock carried withP, is given by the following formula: [35]

t= (1 - 3GM/(rc2))1/2tR. (TD)*

In this revised formula, G is the Newtonian gravitational constant,

whilst ris the radius ofPs orbit and tR is the time as recorded by anexternal observer far distant from the orbit ofP. In POAMS, thisexternal time, is the zero end of the scale of time-dilations, calleddeep space time (DST) [36]. This formula provides the basis forcalculations which predict that clocks in the Global PositioningSatellites orbiting the Earth should run faster relative to Earthclocks. The amount predicted agrees very closely with what isactually observed [37]. The orbital time dilation formula (TD)* is thesame as predicted by General Relativity, except that in Einsteinstheory, rdoes not measure exactly the radius of the orbit [38].

POAMS, then, as does General Relativity, predicts that time isdilated, not only by speed but also in the free orbital motion in thepresence of a massive body. The analysis in reference 35 showsthat even ifP is relatively stationary in the vicinity ofB, there is atime dilation effect given by

t= (1 - 2GM/(rc2))1/2tR.

A clock on the surface of the Earth will therefore run more slowly

than a clock which is not subjected to Earths influence. However,the mass of the Earth is not large enough to have an appreciable


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effect on the passage of time. Specifically, the clock on Earth losesroughly 10-9 seconds in an hour, which is scarcely noticeable [2].Much larger, more massive bodies will have a significant effect oneven stationary clocks.

More generally, let us now consider the case in which the particle Pmoves in a non-circular orbit about the body B. Again, B is assumedto be perfectly spherical and spinless. Since Ps orbit is not a circle,the radial distance, r, ofP from B depends on the angle, , whichthe radial axis ofPmakes with some fixed axis any at point. In thisgeneral case, it can be shown that the proper time, t, recorded onPs clock relative to DST, tR, is given by

c2dt2 = c2F(r)dtR2- (1/F(r))dr2-r2d2, (TD)**

where F(r) = 1 2MG/rc2 [39]. This is the same formula that isderived in General Relativity, being the metric for the equatorialplane of what is called Schwarzschild space-time[40]. As in GeneralRelativity, the formula (TD)** can be thought of as determining thespace-time geometry surrounding a spinless spherical body. Again,as in General Relativity, it can be shown that this space-timegeometry determines that a freely moving particle P in an almostclosed orbit about the body B follows an elliptical orbit, theperihelion (the point of closest approach of P to B) of whichadvances very slowly in the manner of a Spirograph [41].

It can be shown that from the equations of motion for freely movingparticles associated with (TD)**, in the formalism of POAMS theorbital angular momentum of P relative to B is conserved.Newtonian theory cannot produce such an orbit since such an orbitcannot be derived from an inverse square law involvinggravitational force[39]. In this way, the POAMS equations of motionare more general than Newtons and are able to derive at least oneof the space-times projected by General Relativity.

Section 13: Stellar Collapse and Black Holes

We turn now to the end point in the evolution of stars and, inparticular, stellar collapse, which, according to certain theoriesopens up the possibility of time travel. Theory and observation tellus that certain types of stars implode at the end of their life andshrink in size towards a white dwarf state, whilst others explode toform supernovas. Some theories predict that stars of a certaincritical mass continue to shrink to a critical radius. In this case,General Relativity predicts that such a star will continue to collapse

to form a space-time singularity. This, it is said, is a region in


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which the fabric of space-time is literally torn apart by theenormous gravitational effects caused by the collapsing star.

In General Relativity, with its interpretation of light travelling asphotons, it is possible for light to be bent due to gravitational

effects on those alleged particles [42]. In the scenario of a starcollapsing to a point just described, the implication is that thesegravitational effects are so enormous that light inside the regiondetermined by the critical radius is so bent that it cannot escape tothe outside region. The physical implication of this is that thecollapsed star is invisible to any external observer and hence theterm black hole was introduced to describe this final stage ofstellar collapse [43].

As a particular example, in Einsteinian General Relativity, the

external space-time geometry of a collapsing non-rotating sphericalstar is described, as we have seen, by Schwarzschild space-time. Inthis theory it is possible for such a star, given that it has a certaincritical mass, to shrink in size to its Schwarzschild radius,r = 2MG/c2 [44]. Having reached this critical radius, according toGeneral Relativity it is possible for the star to shrink to a radius ofless than 2MG/c2, so that the signs of dtR

2 and dr2 in (TD)** areinterchanged. In this case, mathematics tells us that the radius rbecomes a time-like variable. Since no physical effect can halt themonotonic increase of such a variable, the implication in General

Relativity is that once a star has collapsed through its Schwarzschildradius, it continues to collapse to form a space-time singularity atthe radius r= 0. According to (TD)**, this is a point at which thetime is infinitely dilated.

In the General Relativistic scenario of a black hole just described, afreely moving space-traveller, in his own proper time, can reach theSchwarzschild radius surrounding the black hole in finite time andfall in. Once he enters this region, he suffers the same fate as thecollapsed star and can never return. He will be torn apart by the

enormous gravitational effects long before he reaches the space-time singularity at r= 0. On the other hand, according to the clockof an external observer who remains at a safe distance, the space-traveller can never actually reach the Schwarzschild radius, sincefrom (TD)**, time is infinitely dilated there. From this we mayconclude that the existence of a black hole in the above sense cannever be verified by means of any physical experiment, for if anobserver enters within the Schwarzschild radius to verify theexistence of the space-time singularity, he can never return tocommunicate his results! In this way, the space-time singularity at

r= 0 is surrounded by what is esoterically called an event horizonat the Schwarzschild radius.


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Before we continue, it needs to be stressed that what we sayconcerning black holes depends very much on how such entitiesare defined. The original meaning of the term black hole, firstcoined by Laplace in the eighteenth century [45], was simply a namefor a centre of mass so large that light cannot escape itsgravitational effects and so is effectively invisible. We shall takethe term also as implying the existence of a space-time singularitysince, in our Normal Realist view, the concept of such an absurdityis in conflict with common sense. More formally, we take a blackhole, as in General Relativity, to mean the region contained withinthe event horizon.

It needs to be stressed that a black hole is a product purely ofmathematical theory, and although it generates much speculative

interest, as a meaningfully real physicalobject it has no place in ourNormal Realist philosophy. This is because, as we have explained, inthe case of a collapsing non-rotating star, the theoretical existenceof the black hole can in no way whatsoever be empirically verified.In effect, the event horizon conceals the singular core from anypossible observation. The only observable facets of such an objectwould lie in any effects it might have on its surroundings, and sucheffects may well have other logical explanations.

Be that as it may, Schwarzschild space-time does produce some

practical consequences. Derived in General Relativity as a specificsolution of the Einstein Field Equations it provides a good model ofour solar system in that it predicts physical effects which agree withempirical and observational evidence. However, it must be recalledthat the same model can be produced by POAMS [39]. Although thismodel predicts all the observable phenomena within our solarsystem, and so is a good theoretical model, there is no compellingreason for supposing that this model will accurately predict whatmay happen at the end point of stellar evolution.

As explained in reference 39, the POAMS derivation of what isessentially the Schwarzschild metric, (TD)**, depends ultimately onthe time dilation formula for circular motion, (TD)*, so that r isgreater than 3MG/c2 in (TD)**. Remember that in POAMS, (TD)**amounts to the general time dilation formula along the pathfollowed by any freely moving material particle in the otherwiseempty space surrounding an ideally spherical, spinless body. Hence,in contrast to General Relativity, in which (TD)** is simply a solutionto the Field Equations with no restriction on the value of r(exceptthat it cannot be negative), in POAMS, there is a definite built-in

restriction, in (TD)**

, on the values ofr. In other words, in POAMS,there is no reason to suppose that the theoretical Schwarzschild


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radius is ever actually reached in stellar collapse, let alone thepredicted space-time singularity at r= 0. This means, of course,that the same practical consequences that are claimed on behalf ofGeneral Relativity follow equally from POAMS but without any ofthose mysterious singularities that are invoked by General

Relativity. (It is worth noting, here, perhaps, that a synonym forsingularity is absurdity.)

There are other space-times predicted by General Relativity,besides this Schwarzschild space-time, which are taken to imply theexistence of black holes. For example, the case of a rotating star ismodelled on Kerr space-time [46]. In this scenario when the starcollapses to form a black hole, rather than the enclosed space-time singularity being formed as a point, there is a ring singularityof a particular radius enclosed within two event horizons. It is now

generally accepted in General Relativity that any rotating star whichcollapses to form a black hole will eventually settle down to astationary state described by the Kerr solution. Moreover, the sizeand shape of this black hole depends only on its mass and rate ofrotation, not on the nature of the body from which it has collapsed:this claim is famously paraphrased as, a black hole has no hair [47][48].

Now it is not necessary for us to examine every possible theory inorder to provide the Normal Realist arguments against the physical

existence of black holes. The Normal Realist philosophy is basedfirmly on observation and, as we have said, the very nature of thetheoretically alleged black hole prevents its existence from beingempirically verified since observational communication with anyoutside observer is prevented by the presence of the event horizon.So when scientists claim that there is experimental evidence for theexistence of a black hole, what they really mean is not that blackholes have been observed but that what is actually observed arecertain phenomena which could, in theory, have been caused by thepresence of a black hole. So from the Normal Realist point of view,

we stress that black holes cannot exist as physical objects sincethere is absolutely no empirical evidence whatsoever for theirexistence. It is to be borne in mind, therefore, that these blackholes are purely theoretical predictions of General Relativity andthat there are many alternative theories which do not predict thepresence of these space-time singularities[49].

The Holy Grail for the believers in the existence of black holes hasalways been the binary star system, Cygnus X-1. This systemconsists of a star together with an invisible companion. If one star

of such a binary system were a black hole, then it would accretematter from its visible companion. Theory predicts that this would


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form a gaseous disc around the black hole, which would becomehot enough to produce intense bursts of X-rays. Such bursts of X-rays were first detected coming from Cygnus X-1 in 1971[50]. InPOAMS, we have an alternative argument to explain thephenomenon in Cygnus X-1, based purely on angular momentum

considerations in short, that all ordinary angular momentumsystems have barycentres which, in themselves, are the eyes ofvortices such as whirlpools, cyclones and spiral galaxies [51]. Thereare, of course, other claimed evidences of the existence of blackholes, as, for example, in the case of the data supplied by the radiogalaxy M87. But again, this so-called evidence can be disputed onthe same rational grounds.

Many physicists, then, regard the predicted existence of space-timesingularities in General Relativity as being, not evidence for the

existence of real cosmic sinkholes but rather as an indication of thefact that General Relativity is not valid at a small enough scale; forexample, at the end point of stellar collapse. In other words, theyregard General Relativity as an incomplete theory. We agree withthis sentiment. In POAMS, as has been shown, we have argued that(TD)**, for example, may not be valid for rless than 3MG/c2. Also,in POAMS, space-time is ultimately discrete on a small enough,analytical scale. This addresses the widely held view that GeneralRelativity and Quantum Mechanics must somehow be amalgamatedin order to produce a better model of observed physical

phenomena. Some of these physicists argue that a quantisedversion of General Relativity would perhaps prevent space-timesingularities from occurring [52]. Many highly contrived theories,therefore, are claimed to have succeeded in reconciling the two. Incontrast to these contrivances, the Angular Momentum Synthesis ofPOAMS includes a version of Relativity which is quantisedthroughout every root and branch.

Section 14: Wormholes in Space-time and Time Travel

We have shown that according to our Normal Realist approach touniform motion, time travel into the future is at least theoreticallypossible to a limited extent according to the time dilation formula.This possibility presents no logical or moral difficulty. But whatabout the possibility of time travel in the more general setting ofPOAMS and General Relativity?

As stated earlier, in POAMS, as in General Relativity, the space-timegeometry is non-Euclidean since the path of a freely moving particleis curved. In General Relativity this non-standard geometry leads to

the purely mathematicalpossibility of the existence of wormholesin space-time which connect one part of space-time to another. This


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possibility is projected essentially because General Relativitymaintains that space-time becomes so warped due to the presenceof matter that distinct regions may be interconnected. This isanalogous to an ordinary sheet of paper being bent so that its topand bottom touch. This idea was first put forward by Einstein and

Rosen in 1935 and wormholes were originally termed Einstein-Rosen bridges [53]. The idea is that these twists in the fabric ofspace-time occur due to enormous gravitational effects, and so canoccur only in the neighbourhood of a space-time singularity. Sincethese wormholes connect one distant event to another, which ofcourse, involves time as well as space, their theoretical existenceopens up the possibility of time travel, both into the future and thepast! Such an idea has formed the basis of many good stories forscience fiction writers and film makers alike!

Certainly, General Relativity allows the possibility, in theory at anyrate, of a wormhole in the case of gravitational collapse, whenspace-time singularities are formed. In the case of theSchwarzschild model for a non-rotating black hole, it is notpossible for a space-traveller, once through the event horizon, toavoid the space-time singularity. So even if the wormhole wasthere, the traveller would not be able to pass through. However, inthe case of the Kerr model for a rotating black hole it istheoretically possible for a traveller to avoid the space-timesingularity and pass through a wormhole, thereby travelling in

time as well as space [46].

We have already discussed the problems associated with time travelinto the past. It is important to note, however, that even if it werepossible to pass through a wormhole connected to another event inspace and time, this does not necessarily imply the possibility ofclosed time-like curves whereby a traveller could end up at thesame point in space but back in his own past. For example, thephysical laws which might enable a traveller to pass through awormhole may be such that they always restrict the traveller to

arriving at an event at a point some distance away from where hestarts out, so that he cannot interact with his earlier self at thesame point. Some theorists have even gone so far as to suggestthat there is a multiplicity of space-times sprouting fromwormholes, so that a traveller can never end up in his own past!

So now, from our Normal Realist point of view let us examine thispossibility of time travel through these alleged wormholes in space-time. Mathematical models are clearly worthy of study in their ownright and project many interesting theoretical possibilities. The

problem comes when some of these theoretical possibilities areentertained as physical fact. It should come as no surprise to learn


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that there is no place for wormholes in POAMS, since there is noempirical evidence whatsoever for their existence. In our view, evenin General Relativity, they simply pose interesting mathematicalpossibilities of particular space-times which are solutions of theEinstein Field Equations. To interpret such mathematical

extrapolations as physical fact is far-fetched to say the very least.However, in POAMS, this mathematical possibility cannot occur eventheoretically. We have previously stated there are no space-timesingularities in POAMS since the various time dilation formulae arenot valid at the level of quanta, where space-time is ultimatelydiscrete, so that at that ultimate analytical level otherconsiderations have to be taken into account, which preclude thosepossibilities. Even in widely supported theories, such as QuantumGravity, the existence of space-time singularities remains highlydubious. Without such singularities, there can be no possibility of

wormholes. In General Relativity, the mathematical possibility ofwormholes occurs simply as an extrapolation of the space-timegeometry which forms the basis of the mathematical model. Bycontrast, in POAMS, there are no such extrapolations since POAMSrelies on a model based on observation, with time dilation playing afundamental role. In other words, in POAMS there is no physicalreality assigned to a curved space-time manifold as such.


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Part 4: Space and Time on a Cosmological Scale

Section 15: The Nature of Space on a Cosmological Scale

We turn now to the consideration of space and time on a very largescale a cosmologicalscale. We have shown how time is dilated inboth uniform and orbital motion. This leads to questions regardingthe nature oftime in the cosmos, but first let us consider the natureofspace on that cosmological scale. In order to do this, we need tomake clear the meaning of the word universe, at least from ourNormal Realist point of view.

From the time of the Greek Eleatic cosmologists, the word universe

has been taken to mean everything there is in what they conceivedas an everlasting and unchanging (i.e., overall-conserved) unity, orwhole [54]. Following from this Eleatic basis, we shall take theuniverse to mean the all-encompassing whole. In other words,the universe consists ofallthe stars, planets, life-forms, interstellardebris, all energy, time and space, etc. etc., excluding nothingwhatsoever.

Prior to the time of Copernicus, the space in which we live wasthought to have a natural boundary. This natural boundary wasremoved when Earth was no longer regarded as the centre of theuniverse. Following from that time, space was thought to be infiniteand everlasting. This view was reinforced by Newtons concept ofabsolute space, that is to say, infinite three-dimensional Euclideanspace. Initially, Newton proposed that the universe consisted of afinite a

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The Nature of Time Anthony Osborne